Question: Rewrite as a simplified fraction. ${0.8\overline{47} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 847.4747...\\ 10x &= 8.4747...\end{align*}}$ Subtracting the two equations, we have: ${990x = 839}$ ${x = \dfrac{839}{990}} $